Rumours of a move to Wales emerged recently but Mowbray is confident of hanging on to the 24-year-old.
"Everybody does have his price and I wouldn't say there is nothing in it," Mowbray is quoted as saying in the Evening Gazette.
"There have been enquiries for two years for Marvin from Swansea, ever since he went out on loan.
"And yet Marvin has got, I think, three-and-a-half years left on his contract here. There is no reason for us to rush into selling Marvin Emnes. Let's wait and see what the week brings."
Boro currently occupy sixth place in the Championship courtesy of two wins in their opening three league games.